Answer:
Approximately [tex]2.96\; {\rm s}[/tex]. (Assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex] and that air resistance is negligible.)
Explanation:
As the rocket ascends, kinetic energy is converted into gravitational potential energy. When the rocket reaches the highest point, the gravitational potential energy of the rocket would be maximized, while kinetic energy would be minimized- with vertical velocity becoming [tex]v = 0\; {\rm m\cdot s^{-2}}[/tex].
Under the assumptions, velocity of the rocket would change at a rate of [tex]a = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex].
It is given that the initial velocity of the rocket was [tex]u = 29\; {\rm m\cdot s^{-1}}[/tex]. The velocity change would be:
[tex]\Delta v = v - u = (0 - 29)\; {\rm m\cdot s^{-1}}) = (-29)\; {\rm m\cdot s^{-1}}[/tex].
(Negative since the velocity of the rocket is becoming smaller.)
To find the time required to reach this position, divide the change in velocity by the acceleration:
[tex]\begin{aligned} t &= \frac{\Delta v}{a} \\ &= \frac{(-29)\; {\rm m\cdot s^{-1}}}{(-9.81)\; {\rm m\cdot s^{-2}}} \\ &\approx 2.96\; {\rm s}\end{aligned}[/tex].
